Finite element methods (FEM) have emerged as a versatile and robust framework for the numerical simulation of evolving partial differential equations (PDEs). These methods discretise complex ...

Covers finite difference, finite element, finite volume, pseudo-spectral, and spectral methods for elliptic, parabolic, and hyperbolic partial differential equations. Prereq., APPM 5600. Recommended ...

We propose a hybrid spatial finite-difference/pseudospectral discretization for European option-pricing problems under the Heston and Heston–Hull–White models. In ...

We study the effect of numerical quadrature in space on semidiscrete and fully discrete piecewise-linear finite element methods for parabolic integrodifferential ...

One of the common classes of equations that is encountered in several branches of science is partial differential equations. So in this article, I look at a software package called FreeFem++ that is ...

SIAM Journal on Numerical Analysis, Vol. 26, No. 6 (Dec., 1989), pp. 1474-1486 (13 pages) An explicit finite difference algorithm is developed to approximate the solution of a nonlinear and nonlocal ...

Description: Ordinary differential equations and methods for their solution, including series methods and the Laplace transform. Applications of differential equations. Systems, stability, and ...

General aspects of polynomial interpolation theory. Formulations in different basis, e.g. Lagrange, Newton etc. and their approximation and computational properties ...

It is a pleasure to introduce the latest issue of The Journal of Computational Finance. The first two contributions focus on using novel neural network machinery to enhance classical financial ...